In 1864 Skærbæk became part of Germany due to consequences of the Second Schleswig War. In 1876 he received his medical doctorate from the University of Copenhagen, and in 1879 became an assistant to Edmund Hansen Grut (1831-1907) at the Havnegade eye clinic. After Grut"s retirement in 1896, he became director of the clinic, as well as being the second professor of ophthalmology at the University of Copenhagen, a position he would maintain until his retirement in 1910.
Bjerrum made contributions regarding pathogenetic research of glaucoma, and performed extensive investigations involving campimetry.
He was interested in the correlation between visual perception of form and the resolving power in localized regions of the retina. He was particularly focused on the subtleties of the central 30° of the visual field rather than the standard perimetry tests that many of his contemporaries favored.
As a result of his campimetric tests he discovered a small glaucomatous scotoma that was to become known as a "Bjerrum scotoma", which is a visual field defect that goes by several other names, such as "sickle scotoma", "arcuate scotoma" or "scimitar scotoma". Other eponyms named after Bjerrum include:
Bjerrum tangent screen: Screen used to assess the central 30° of the visual field
Bjerrum"s area: An arcuate region that extends above and below the blind spot to between 10° and 20° of fixation point.
After Bjerrum"s retirement in 1910, his work in campimetry was continued by his assistant, Henning Rønne (1878-1947).